Why the Cosmological Constant Problem is Hard

TL;DR

This paper examines why the cosmological constant problem remains difficult, highlighting that bulk supersymmetry in brane world models does not necessarily prevent a non-zero brane cosmological constant due to a mass gap effect.

Contribution

It demonstrates that in brane world scenarios with infinite volume extra dimensions, bulk supersymmetry does not guarantee a zero brane cosmological constant because of a mass gap in bulk graviton modes.

Findings

Bulk supersymmetry does not protect the brane cosmological constant.

A mass gap causes the effective four-dimensional behavior at large distances.

The distance scale for this effect is set by the brane cosmological constant.

Abstract

We consider a recent proposal to solve the cosmological constant problem within the context of brane world scenarios with infinite volume extra dimensions. In such theories bulk can be supersymmetric even if brane supersymmetry is completely broken. The bulk cosmological constant can therefore naturally be zero. Since the volume of the extra dimensions is infinite, it might appear that at large distances one would measure the bulk cosmological constant which vanishes. We point out a caveat in this argument. In particular, we use a concrete model, which is a generalization of the Dvali-Gabadadze-Porrati model, to argue that in the presence of non-zero brane cosmological constant at large distances such a theory might become effectively four dimensional. This is due to a mass gap in the spectrum of bulk graviton modes. In fact, the corresponding distance scale is set precisely by the brane cosmological constant. This phenomenon appears to be responsible for the fact that bulk supersymmetry does not actually protect the brane cosmological constant.